Fast algorithm for zero-phase linear filter using discrete cosine transform

This Letter deals with a practical signal processing problem where the filter is zero-phase and is specified by the frequency response. The authors show that if the signal is symmetrically extended, then the fast Fourier transform (FFT)-based algorithm can be efficiently implemented by using the discrete cosine transform without signal extension. They extend the proposed algorithm to 2D filters and show that computationally it is at least four times more efficient than the FFT-based algorithm. A practical application of the new algorithm is a fast Wiener inverse filter, which is used to estimate images taken under the condition of air turbulence.